Kumar spent $240 of his allowance on food and 20% of the remaining allowance on transport. He spent 68% of his allowance on food and transport. What percentage of his allowance did he spend on transport?
(1) 48%
(2) 32%
(3) 8%
(4) 4%
Let's suppose Kumar's total allowance is x.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent 20% of the remaining allowance on transport, so he spent 0.20(0.32x) = 0.064x on transport.
We know that he spent $240 of his allowance on food, so we can set up the equation 0.68x - 240 = 0.064x.
Simplifying this equation, we get 0.616x = 240.
Dividing both sides by 0.616, we find x ≈ 389.610.
To find the percentage of his allowance he spent on transport, we can calculate (0.064x / x) × 100 ≈ 6.4%.
Therefore, the answer is (4) 4%.
How to get (3) 8%?
Apologies for the mistake in my previous response. Let's go through the problem again to find the correct answer.
Let Kumar's total allowance be x.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent $240 of his allowance on food, so we can set up the equation 0.68x = 240.
Solving for x, we find x ≈ 352.941.
Now, to find the percentage of his allowance he spent on transport, we can calculate (0.32x / x) × 100 ≈ 9.09%.
Therefore, the correct answer is not among the given answer choices.
To find the percentage of Kumar's allowance spent on transport, we need to follow a step-by-step approach. Let's break down the problem and solve it systematically.
1. Kumar spent $240 of his allowance on food.
2. The remaining allowance after spending on food is not mentioned directly, so we need to calculate it.
- Let's assume Kumar's total allowance is A dollars.
- Kumar spent $240 on food, so the remaining allowance will be A - 240 dollars.
3. Kumar spent 20% of the remaining allowance on transport.
- To find this amount, we need to calculate 20% of (A - 240).
- 20% can be written as 0.2 in decimal form.
- So, the amount spent on transport is 0.2 * (A - 240) dollars.
4. Kumar spent a total of 68% of his allowance on food and transport combined.
- This means that the sum of the amounts spent on food and transport is equal to 68% of his allowance.
- Mathematically, this can be represented as:
$240 + 0.2 * (A - 240) = 0.68 * A
5. Now, we can solve the equation to find the value of A and then determine the percentage spent on transport.
- Expanding the equation:
$240 + 0.2A - 48 = 0.68A
- Combining like terms:
0.2A - 0.68A = 48 - $240
-0.48A = -$192
- Dividing both sides by -0.48:
A = -$192 / (-0.48)
A ≈ $400
6. We have found that Kumar's total allowance is approximately $400.
7. Now, we can calculate the amount spent on transport:
- 20% of (A - 240) = 0.2 * ($400 - $240) = 0.2 * $160 = $32
8. Finally, to find the percentage of Kumar's allowance spent on transport, we divide the amount spent on transport by the total allowance and multiply by 100:
- Percentage spent on transport = ($32 / $400) * 100 ≈ 8%
Therefore, the correct answer is option (3) 8%.
Apologies for the previous incorrect responses. You are correct, the percentage of Kumar's allowance spent on transport is 8%, as calculated step by step above. Thank you for pointing out the error, and I apologize for any confusion caused.
Let's find the amount Kumar spent on food first:
He spent 68% of his allowance on food and transport, so the amount spent on food is 68% of the allowance.
Let's say the allowance is x dollars.
Amount spent on food = 68% of x
= (68/100) * x
= 0.68x
Now, we know that Kumar spent $240 on food, so we can set up an equation:
0.68x = $240
Divide both sides by 0.68:
x = $240 / 0.68
x ≈ $352.94
So, the allowance is approximately $352.94.
Now, let's find the amount Kumar spent on transport:
He spent 20% of the remaining allowance on transport.
Remaining allowance after spending on food = x - $240
Remaining allowance after spending on food = $352.94 - $240
Remaining allowance after spending on food ≈ $112.94
Amount spent on transport = 20% of remaining allowance
= 20% of $112.94
= (20/100) * $112.94
= $22.59
Now, let's find the percentage of his allowance Kumar spent on transport:
Percentage of allowance spent on transport = (amount spent on transport / allowance) * 100
= ($22.59 / $352.94) * 100
≈ 6.4%
Therefore, Kumar spent approximately 6.4% of his allowance on transport.
The closest option is (3) 8%, so the correct answer is (3) 8%.
To calculate the percentage of Kumar's allowance spent on transport, we need to follow these steps:
Step 1: Calculate the amount Kumar spent on food.
We know that Kumar spent 68% of his allowance on food and transport. Since we are given that he spent $240 on food, we can use this information to find the total allowance.
Let's represent the total allowance as A.
So, 68% of A = $240.
To solve for A, we divide both sides of the equation by 68 and then multiply by 100 to express it as a percentage:
68A/100 = $240
A = ($240 * 100) / 68
Therefore, A ≈ $352.94.
Now, since we know the total allowance is $352.94 and Kumar spent $240 on food, we can find the remaining allowance by subtracting the amount spent on food from the total allowance:
Remaining allowance = Total allowance - Amount spent on food
Remaining allowance = $352.94 - $240
Remaining allowance ≈ $112.94
Step 2: Calculate the amount Kumar spent on transport.
We are given that Kumar spent 20% of the remaining allowance on transport. To find the amount spent, we multiply the remaining allowance by 20%:
Amount spent on transport = Remaining allowance * 20%
Amount spent on transport ≈ $112.94 * 20%
Amount spent on transport ≈ $22.59
Step 3: Calculate the percentage of Kumar's allowance spent on transport.
To find the percentage, we divide the amount spent on transport by the total allowance and multiply by 100:
Percentage spent on transport = (Amount spent on transport / Total allowance) * 100
Percentage spent on transport ≈ ($22.59 / $352.94) * 100
Percentage spent on transport ≈ 0.064 * 100
Percentage spent on transport ≈ 6.4%
Therefore, Kumar spent approximately 6.4% of his allowance on transport.
Comparing this with the answer choices:
(1) 48%
(2) 32%
(3) 8%
(4) 4%
None of the given answer choices match the calculated percentage of 6.4%.